In brief:
Ligament tear

There are may degrees of tear. A sprained ankle always involve the tear of thousands or hundreds of thousands of ligament fibers.

A cast sometime is needed to immobilize the ankle 100% so to facilitate recovery (cast for 3 weeks to 1 month, once indicated). A surgery is needed when there tear is so severe (that the ankle can remain very unstable forever) that the ankle lost its function.

In brief:
Ligament tear

There are may degrees of tear. A sprained ankle always involve the tear of thousands or hundreds of thousands of ligament fibers.

A cast sometime is needed to immobilize the ankle 100% so to facilitate recovery (cast for 3 weeks to 1 month, once indicated). A surgery is needed when there tear is so severe (that the ankle can remain very unstable forever) that the ankle lost its function.
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